Divide by a Fraction

Date: 03/19/97 at 18:05:06
From: James Farrell
Subject: Divide by a Fraction

Dear Dr. Math,

	How do you divide a whole number by a fraction?  Consider:

   5
--------
   1
  ---
   2


If you express it as:

   5
  ---
   1                 5         2
--------      =     ---   x   ---    =    10
   1                 1         1
  ---
   2

Why did I end up with 10?  I'm sure the answer should be 2.5.  Where 
did I go wrong?

Thanks,
Tim Farrell

Date: 03/21/97 at 04:19:54
From: Doctor Mitteldorf
Subject: Re:  Divide by a Fraction

Dear Tim,

Lots of people find this confusing.  If you divide 5 by 2, the 
answer is 2.5.  If you divide 5 by 1/2, do you expect the same thing 
as dividing by 2?

If you divide by a number bigger than 1, it always reduces the 
number. If you divide by 1, it doesn't change anything.  Does that 
make you think that dividing by a fraction less than 1 should INCREASE 
the number?

How many kids can you serve with 5 cookies if each kid gets 2 cookies? 
You can serve 2 kids (with enough left over for 1/2 a kid).  

How many kids can you serve with 5 cookies if each kid gets 1/2 a 
cookie?  That's 5 divided by 1/2.

-Doctor Mitteldorf,  The Math Forum
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